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Étude des sous-variétés dans les variétés kählériennes, presque kählériennes et les variétés produit / Study of submanifolds of Kaehler manifolds, nearly Kaehler manifolds and product manifoldsMoruz, Marilena 03 April 2017 (has links)
Cette thèse est constituée de quatre chapitres. Le premier contient les notions de base qui permettent d'aborder les divers thèmes qui y sont étudiés. Le second est consacré à l'étude des sous-variétés lagrangiennes d'une variété presque kählérienne. J'y présente les résultats obtenus en collaboration avec Burcu Bektas, Joeri Van der Veken et Luc Vrancken. Dans le troisième, je m'intéresse à un problème de géométrie différentielle affine et je donne une classification des hypersphères affines qui sont isotropiques. Ce résultat a été obtenu en collaboration avec Luc Vrancken. Et enfin dans le dernier chapitre, je présente quelques résultats sur les surfaces de translation et les surfaces homothétiques, objet d'un travail en commun avec Rafael López. / Abstract in English not available
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Superfícies CMC em variedades tridimensionais : diferencial de HopfNicoli , Adriana Vietmeier January 2014 (has links)
Orientador: Prof. Dr. Sinuê Dayan Barbero Lodovici / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática, 2014. / O objetivo principal deste texto é apresentar o teorema de Hopf 3.16 nos espaços R3, H3
e S3, resultado clássico sobre superfícies com curvatura média constante (CMC). Antes
disto, apresentamos alguns conceitos importantes de Geometria Diferencial, entre eles
o Teorema de Gauss-Bonnet 2.13 e o Teorema de Hadamard 2.36. Por fim, de maneira
breve, enunciamos o teorema de Hopf em espaços produto (H2XR e S2XR). / The main objective of this paper is to present the Hopf's theorem (3.16) in spaces R3,
H3 and S3, a classical result on surfaces with constant mean curvature (CMC). Before
this, we present some important concepts of Differential Geometry, including the Gauss-
Bonnet Theorem (2.13) and Hadamard's Theorem (2.36). Finally, and briefly, we state
the Hopf's theorem in product spaces (H2XR and S2XR).
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Espectro essencial de uma classe de variedades riemannianas / Essential spectrum of a class of Riemannian manifoldsLuiz AntÃnio Caetano Monte 21 November 2012 (has links)
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Neste trabalho, provaremos alguns resultados sobre espectro essencial de uma classe de variedades Riemannianas, nÃo necessariamente completas, com condiÃÃes de curvatura na vizinhanÃa de um raio. Sobre essas condiÃÃes obtemos que o espectro essencial do operador de Laplace contÃm um intervalo. Como aplicaÃÃo, obteremos o espectro do operador de Laplace de regiÃes ilimitadas dos espaÃos formas, tais como a horobola do espaÃo hiperbÃlico e cones do espaÃo Euclidiano. Construiremos tambÃm um exemplo que indica a necessidade das condiÃÃes globais sobre o supremo das curvaturas seccionais fora de uma bola para que a variedade nÃo tenha espectro essencial. / In this thesis we consider a family of Riemannian manifolds, not necessarily complete, with curvature conditions in a neighborhood of a ray. Under these conditions we obtain that the essential spectrum of the Laplace operator contains an interval. The results presented in this thesis allow to determine the spectrum of the Laplace operator on unlimited regions of space forms, such as horoball in hyperbolic space and cones in Euclidean space. Also construct an example that shows the need of global conditions on the supreme sectional curvature outside a ball, so that the variety has no essential spectrum.
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Volumes e curvaturas médias na geometria de Finsler:superfícies mínimas / Volumes and means curvatures in Finsler geometry: minimal surfacesChavéz, Newton Mayer Solorzano 16 April 2012 (has links)
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Previous issue date: 2012-04-16 / In Finsler geometry, we have several volume forms, hence various of mean curvature
forms. The two best known volumes forms are the Busemann-Hausdorff and Holmes-
Thompson volume form. The minimal surface with respect to these volume forms are
called BH-minimal and HT-minimal surface, respectively. Let (R3; eFb) be a Minkowski
space of Randers type with eFb = ea+eb; where ea is the Euclidean metric and eb = bdx3;
0 < b < 1: If a connected surface M in (R3; eFb) is minimal with respect to both volume
forms Busemann-Hausdorff and Holmes-Thompson, then up to a parallel translation of
R3; M is either a piece of plane or a piece of helicoid which is generated by lines screwing
along the x3-axis. Furthermore it gives an explicit rotation hypersurfaces BH-minimal
and HT-minimal generated by a plane curve around the axis in the direction of eb] in
Minkowski (a;b)-space (Vn+1; eFb); where Vn+1 is an (n+1)-dimensional real vector
space, eFb = eaf eb
ea ; ea is the Euclidean metric, eb is a one form of constant length
b = kebkea; eb] is the dual vector of eb with respect to ea: As an application, it give us an
explicit expression of surface of rotation “ forward” BH-minimal generated by the rotation
around the axis in the direction of eb] in Minkowski space of Randers type (V3; ea+eb): / Na Geometria de Finsler, temos várias formas volume, consequentemente várias formas
curvaturas médias. As duas mais conhecidas são as formas de volumes Busemann-
Hausdorff e Holmes-Thompson. As superfícies mínimas com respeito a estes são chamados
superfícies BH-mínimas e HT-mínimas, respectivamente. Seja (R3; eFb) um espaço
de Minkowski do tipo Randers com eFb = ea+eb; onde ea é a métrica Euclidiana e
eb = bdx3;0 < b < 1: Uma superfície em (R3; eFb) conexa M é mínima com respeito a ambas
formas volumes Busemann-Hausdorff e Holmes-Thompson, então a menos de uma
translação paralela de R3; M é parte de um plano ou parte de um helicóide, a qual é gerada
pela rotação de uma reta (perpendicular ao eixo x3) ao longo do eixo x3: Ademais podemos
obter explicitamente hipersuperfícies de rotação BH-mínima e HT-mínima geradas
por uma curva plana em torno do eixo na direção de eb] num espaço (a; b) de Minkowski
(Vn+1; eFb); onde Vn+1 é um espaço vetorial de dimensão (n+1); eFb = eaf eb
ea ; ea é a
métrica Euclidiana, eb é uma 1-forma constante com norma b := kebkea; eb] é o vetor dual
de eb com respeito a a: Como aplicação, se dá uma expressão explícita de superfície de
rotação completa “forward” BH-mínima gerada pela rotação em torno do eixo na direção
de eb] num espaço de Minkowski do tipo Randers (V3; ea+eb):
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Um caso particular da desigualdade de Heintze e KarcherMota, Andrea Martins da 15 September 2014 (has links)
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Previous issue date: 2014-09-15 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The objective of this notes is to prove in detail a theorem, due to Ernst
Heintze and Hermann Karcher, establishing an upper bound for the volume of
compact domains in a connected closed hypersurface immersed in Euclidean
space E. As application we will give an alternative proof of the Alexandrov’s
theorem, which states that the Euclidean spheres are the only embedded
closed hypersurfaces of constant mean curvature in E. / O objetivo deste trabalho é demonstrar em detalhes um teorema devido
a Ernst Heintze e Hermann Karcher que estabelece uma cota superior para
o volume de domínios compactos em uma hipersuperfície conexa, fechada e
mergulhada no espaço euclidiano E. Como aplicação será dada uma prova
alternativa do Teorema de Alexandrov, que caracteriza as esferas euclidianas
como as únicas hipersuperfícies conexas, fechadas e mergulhadas de curvatura
média constante em E.
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Genericity of bumpy metrics, bifurcation and stability in free boundary CMC hypersurfaces / Genericidade das métricas bumpy, bifurcação e estabilidade em hipersuperfícies de CMC e fronteira livreCárdenas, Carlos Wilson Rodríguez 03 December 2018 (has links)
In this thesis we prove the genericity of the set of metrics on a manifold with boundary M^{n+1}, such that all free boundary constant mean curvature (CMC) embeddings \\varphi: \\Sigma^n \\to M^{n+1}, being \\Sigma a manifold with boundary, are non-degenerate (Bumpy Metrics), (Theorem 2.4.1). We also give sufficient conditions to obtain a free boundary CMC deformation of a CMC inmersion (Theorems 3.2.1 and 3.2.2), and a stability criterion for this type of immersions (Theorem 3.3.3 and Corollary 3.3.5). In addition, given a one-parametric family, {\\varphi _t : \\Sigma \\to M} , of free boundary CMC immersions, we give criteria for the existence of smooth bifurcated branches of free boundary CMC immersions for the family {\\varphi_t}, via the implicit function theorem when the kernel of the Jacobi operator J is non-trivial, (Theorems 4.2.3 and 4.3.2), and we study stability and instability problems for hypersurfaces in this bifurcated branches (Theorems 5.3.1 and 5.3.3). / Nesta tese, provamos a genericidade do conjunto de métricas em uma variedade com fronteira M^{n+1}, de modo que todos os mergulhos de curvatura média constante (CMC) e fronteira livre \\varphi : \\Sigma^n \\to M^{n+1}, sendo \\Sigma uma variedade com fronteira, sejam não-degenerados (Métricas Bumpy), (Teorema 2.4.1). Nós também fornecemos condições suficientes para obter uma deformação CMC e fronteira livre de uma imersão CMC (Teoremas 3.2.1 and 3.2.2), e um critério de estabilidade para este tipo de imersões (Teorema 3.3.3 and Corolario 3.3.5). Além disso, dada uma família 1-paramétrica, {\\varphi _t : \\Sigma \\to M} , de imersões de CMC e fronteira livre, damos os critérios para a existência de ramos de bifurcação suaves de imersões CMC e fronteira livre para a familia {\\varphi_t}, por meio de o teorema da função implícita quando o kernel do operador Jacobi J é não-trivial, (Teoremas 4.2.3 and 4.3.2), e estudamos o problema da estabilidade e instabilidade para hipersuperfícies em naqueles ramos de bifurcação (Teoremas 5.3.1 and 5.3.3).
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THE USE OF 3-D HIGHWAY DIFFERENTIAL GEOMETRY IN CRASH PREDICTION MODELINGAmiridis, Kiriakos 01 January 2019 (has links)
The objective of this research is to evaluate and introduce a new methodology regarding rural highway safety. Current practices rely on crash prediction models that utilize specific explanatory variables, whereas the depository of knowledge for past research is the Highway Safety Manual (HSM). Most of the prediction models in the HSM identify the effect of individual geometric elements on crash occurrence and consider their combination in a multiplicative manner, where each effect is multiplied with others to determine their combined influence. The concepts of 3-dimesnional (3-D) representation of the roadway surface have also been explored in the past aiming to model the highway structure and optimize the roadway alignment. The use of differential geometry on utilizing the 3-D roadway surface in order to understand how new metrics can be used to identify and express roadway geometric elements has been recently utilized and indicated that this may be a new approach in representing the combined effects of all geometry features into single variables. This research will further explore this potential and examine the possibility to utilize 3-D differential geometry in representing the roadway surface and utilize its associated metrics to consider the combined effect of roadway features on crashes. It is anticipated that a series of single metrics could be used that would combine horizontal and vertical alignment features and eventually predict roadway crashes in a more robust manner.
It should be also noted that that the main purpose of this research is not to simply suggest predictive crash models, but to prove in a statistically concrete manner that 3-D metrics of differential geometry, e.g. Gaussian Curvature and Mean Curvature can assist in analyzing highway design and safety. Therefore, the value of this research is oriented towards the proof of concept of the link between 3-D geometry in highway design and safety. This thesis presents the steps and rationale of the procedure that is followed in order to complete the proposed research. Finally, the results of the suggested methodology are compared with the ones that would be derived from the, state-of-the-art, Interactive Highway Safety Design Model (IHSDM), which is essentially the software that is currently used and based on the findings of the HSM.
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Real Time 3d Surface Feature Extraction On FpgaTellioglu, Zafer Hasim 01 July 2010 (has links) (PDF)
Three dimensional (3D) surface feature extractions based on mean (H) and
Gaussian (K) curvature analysis of range maps, also known as depth maps, is an
important tool for machine vision applications such as object detection,
registration and recognition. Mean and Gaussian curvature calculation algorithms
have already been implemented and examined as software. In this thesis,
hardware based digital curvature processors are designed. Two types of real time
surface feature extraction and classification hardware are developed which
perform mean and Gaussian curvature analysis at different scale levels. The
techniques use different gradient approximations. A fast square root algorithm
using both LUT (look up table) and linear fitting technique is developed to
calculate H and K values of the surface described by the 3D Range Map formed
by fixed point numbers. The proposed methods are simulated in MatLab software
and implemented on different FPGAs using VHDL hardware language.
Calculation times, outputs and power analysis of these techniques are compared to
CPU based 64 bit float data type calculations.
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Estimativas para a curvatura mÃdia de subvariedades cilindricamente limitadas / Estimates for the mean curvature of cylindrically bounded submanifoldsAnderson Feitoza LeitÃo Maia 18 February 2013 (has links)
CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Este trabalho à baseado no artigo The Mean Curvature Cylindrically Bounded Submanifolds, nele abordaremos uma estimativa para a curvatura mÃdia de subvariedades completas cilindricamente limitadas. Ademais apresentaremos uma relaÃÃo entre uma estimativa da curvatura mÃdia e o fato de M ser estocasticamente incompleta. / This work is based on the article The Mean Curvature Cylindrically Bounded Submanifolds, it will discuss an estimate for the mean curvature of complete cylindrically submanifolds bounded. Furthermore we present a relationship between an estimate of the mean curvature and the fact that M is stochastically incomplete.
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Desigualdades de Penrose e um teorema da massa positiva para buracos negros carregados / Penrose inequalities and apositive mass theorem for charged black rolesWeslley Marinho LozÃrio 24 February 2014 (has links)
CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Apresentamos desigualdades do tipo Penrose e um teorema de massa positiva para buracos negros carregados, isto Ã, dados iniciais para soluÃÃes tempo-simÃtricas das equaÃÃes de Einstein-Maxwell, que podem ser isometricamente mergulhados no espaÃo euclidiano como grÃficos. As demonstraÃÃes usam uma fÃrmula integral para massa ADM de tais hipersuperfÃcies e o fluxo pela curvatura mÃdia inversa. / We present Penrose-type inequalities and a positive mass theorem to charged black roles, ie, initial data for time-symmetric solutions of the Einstein-Maxwell equations, which can be isometrically immersed in Euclidean space as graphics. The statements use an integral formula for the ADM mass of such hypersurfaces and the inverse mean curvature flow.
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